Skip to main content
Go to the home page of the European Commission (opens in new window)
English English
CORDIS - EU research results
CORDIS

''It’s the Symmetry, Stupid!'' Gearing Up Tensor Networks for the Topological Quantum Revolution

Project description

Computational methods to decode quantum complexity

During the second quantum revolution, understanding topological materials and quantum devices presents a formidable challenge. These quantum systems defy conventional descriptions, lacking local order parameters and exhibiting exotic particle statistics. Despite this, a computational framework is urgently needed to model their behaviour accurately. In this context, the ERC-funded ISYS project aims to harness symmetries and tensor networks. While topological materials defy traditional paradigms, tensor networks unveil a hidden symmetry within entanglement degrees of freedom. This non-invertible symmetry, expressed in bimodule categories, brings abstract concepts to tangible reality. ISYS aims to develop tensor network mathematics, construct computational tools, and bridge categorical symmetries with integrability. This fusion promises real-world applications like renormalisation group flows and quantum error correction.

Objective

This proposal is set in the era of the second quantum revolution, in which there is a strong need for a computational framework to describe and simulate topological materials and quantum devices possessing exotic particle statistics.
* The two leading actors: symmetries and tensor networks.
* The story: while the topological materials seem to defy Landau’s symmetry breaking paradigm as they do not exhibit a local order parameter, tensor networks strike back with the emergence of a local “pulling-through” symmetry of the local tensors describing them.
* The catch: the symmetry happens in the shadow world of entanglement degrees of freedom, is in general non-invertible, and speaks the language of bimodule categories.
* The magic: the tensor network picture makes the abstract concepts and mathematical tools needed to describe topological and critical systems, such as cohomology theory and bimodule categories, very tangible and concrete as wavefunctions of quantum spin systems which can easily be put on a computer.
* The mission: develop the mathematics of tensor network representations of (higher) categorical and non-invertible symmetries; construct a computational toolbox which exploits those symmetries; construct explicit matrix product operator intertwiners for dualities between theories with non-Abelian / categorical symmetries; construct novel CFTs from categorical data; create a bridge between bimodule categories and integrability.
* The crescendo: tensor networks with categorical symmetries take over the world by 1. setting up real-space renormalization group flows in which unwanted relevant perturbations are crushed and 2.constructing and evaluating quantum error correcting codes based on non-Abelian anyons.
* The take-away: deep theoretical ideas and state of the art computational aspects are not parallel lines of development, but are one and the same and must be fused with each other.
* The moral: For things to remain the same, everything must change.

Fields of science (EuroSciVoc)

CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.

You need to log in or register to use this function

Keywords

Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)

Programme(s)

Multi-annual funding programmes that define the EU’s priorities for research and innovation.

Topic(s)

Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.

Funding Scheme

Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.

HORIZON-ERC - HORIZON ERC Grants

See all projects funded under this funding scheme

Call for proposal

Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.

(opens in new window) ERC-2022-ADG

See all projects funded under this call

Host institution

UNIVERSITEIT GENT
Net EU contribution

Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.

€ 2 302 500,00
Address
SINT PIETERSNIEUWSTRAAT 25
9000 Gent
Belgium

See on map

Region
Vlaams Gewest Prov. Oost-Vlaanderen Arr. Gent
Activity type
Higher or Secondary Education Establishments
Links
Total cost

The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.

€ 2 302 500,00

Beneficiaries (1)

My booklet 0 0